Explanation Write the expression for the atmospheric weight of the earth. W air = m air ⋅ g Here, the atmospheric mass of the earth is m air and the acceleration due to gravity is g . Write the expression for the area covered by the earth’s atmosphere. A earth = 4 π R earth 2 Here, the radius of the earth is R earth . Write the expression for the sea level pressure. p sea-level = W air A earth …… (I) Here, the atmospheric mass of the air is W air . Substitute m air ⋅ g for W air and 4 π R earth 2 for A earth in Equation (I). p sea-level = m air ⋅ g 4 π R earth 2 …… (II) Substitute 6.08 × 10 18 kg for m air , 9.81 m / s 2 for g and 6.77 × 10 6 m for R earth in Equation (II). p sea-level = ( 6.08 × 10 18 kg ) ⋅ ( 9.81 m / s 2 ) 4 π ( 6.377 × 10 6 m ) 2 = 59.6448 × 10 18 511 × 10 12 N / m 2 ≈ 117000 Pa The pressure calculated is approximate to the sea-level pressure of 101350 Pa due to the variation in approximate value of the mass of the earth’s atmosphere

8th Edition

ISBN: 9789385965494

Author: Frank White

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 2, Problem 2.24P

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Whether the sea level pressure can be estimated from atmospheric mass of the earth.

Whether the atmospheric mass of the earth can be estimated from the sea level pressure.

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Whether the sea level pressure can be estimated from atmospheric mass of the earth. Whether the atmospheric mass of the earth can be estimated from the sea level pressure.